AcousticsAcoustics

ReverberationReverberation

What is Reverberation?What is Reverberation? ReverberationReverberation is multiple, is multiple,

random, blended random, blended repetitions of a sound.repetitions of a sound.

Three parts:Three parts: Direct Sound, Direct Sound, Early Reflections, & Later Early Reflections, & Later Reflections.Reflections.

Reverberation Time (Decay Reverberation Time (Decay Time)Time) is the time required is the time required for the sound in a room to for the sound in a room to decay 60 dB (also known decay 60 dB (also known as as RT60RT60). This represents a ). This represents a change in sound intensity change in sound intensity or power of 1 million (10 or power of 1 million (10 log 1,000,000 = 60 dB, or log 1,000,000 = 60 dB, or a change in sound a change in sound pressure level of 1,000 (20 pressure level of 1,000 (20 log 1,000 = 60 dB).log 1,000 = 60 dB).

Growth & Decay of SoundGrowth & Decay of Sound

W. C. Sabine, the Harvard W. C. Sabine, the Harvard pioneer in acoustics pioneer in acoustics introduced the concept of introduced the concept of RT60.RT60.

Measuring Reverberation TimeMeasuring Reverberation Time

A common approach to measuring reverberation time. A common approach to measuring reverberation time. Figure B is a more common occurrence than figure A.Figure B is a more common occurrence than figure A.

Measuring Reverberation TimeMeasuring Reverberation Time

The sound sources used to excite the The sound sources used to excite the room must have enough energy room must have enough energy throughout the spectrum to ensure throughout the spectrum to ensure decays sufficiently above the noise to decays sufficiently above the noise to give the required accuracy.give the required accuracy.

Both impulse sources and those giving a Both impulse sources and those giving a steady-state output are used.steady-state output are used.

Impulse SourcesImpulse Sources

Common Common impulse impulse sources are sources are balloon pops balloon pops and starter and starter pistols. The pistols. The diagram shows diagram shows the reverb the reverb decays at decays at several several different octave different octave ranges using a ranges using a starter pistol.starter pistol.

Steady-State SourcesSteady-State Sources

Bands of random Bands of random noise give a noise give a steady and steady and dependable dependable indication of the indication of the average average acoustical effects acoustical effects taking place. taking place.

Octave and 1/3 Octave and 1/3 octave bands of octave bands of random noise random noise (white or pink) (white or pink) are most are most commonly used.commonly used.

Mode Decay VariationsMode Decay Variations The fluctuations in The fluctuations in

the decays result the decays result from beats from beats between closely between closely spaced modes.spaced modes.

The differences in The differences in the four decays is the four decays is due to the random due to the random nature of the noise.nature of the noise.

It is good practice It is good practice to record several to record several decays for each decays for each octave for each mic octave for each mic position of a room.position of a room.

Acoustical flaws Acoustical flaws can often be can often be identified from identified from aberrant decay aberrant decay shapes.shapes.

Room ModesRoom Modes When sound is emitted in a When sound is emitted in a

room with parallel opposing room with parallel opposing walls, the room exhibits a walls, the room exhibits a resonance at a specific resonance at a specific frequency determined by frequency determined by the equation the equation ff00 = 1,130/2L= 1,130/2L (or 565/L), where L is the (or 565/L), where L is the length (in feet) of space length (in feet) of space between the two walls. between the two walls.

A similar resonance occurs A similar resonance occurs at 2fat 2f00, 3f, 3f00, 4f, 4f00, etc., etc.

These resonances are These resonances are called called modesmodes;; specifically, specifically, axial modesaxial modes..

Frequency BeatsFrequency Beats

500 Hz

505 Hz

500 & 505 Hz

Modal Interaction with DecayModal Interaction with Decay The diagram The diagram

shows four shows four different different axial mode axial mode frequencies frequencies in the octave in the octave centered on centered on 63 Hz.63 Hz.

The lower the The lower the frequency, frequency, the less axial the less axial modes there modes there are, so the are, so the more more noticeable noticeable the beats the beats become. become.

Types of Room ModesTypes of Room Modes

Axial modesAxial modes are derived from two walls, are derived from two walls, tangential modestangential modes are derived from four walls, and are derived from four walls, and oblique modesoblique modes are derived from all six surfaces. are derived from all six surfaces.

Frequency EffectFrequency Effect

This diagram This diagram shows typical shows typical fluctuation due to fluctuation due to modal modal interference.interference.

Variation with Mic PositionVariation with Mic Position

There is enough variation of reverb time from There is enough variation of reverb time from one position to another in most rooms to one position to another in most rooms to justify taking measurements at several justify taking measurements at several positions.positions.

The average gives a better statistical picture The average gives a better statistical picture of the behavior of the sound field in the room.of the behavior of the sound field in the room.

If the room is symmetrical, measure only one If the room is symmetrical, measure only one side to minimize time and effort.side to minimize time and effort.

Acoustical CouplingAcoustical Coupling Acoustically coupled Acoustically coupled

spaces are quite spaces are quite common in large public common in large public gathering spaces, but gathering spaces, but are also found in are also found in offices, homes, and offices, homes, and other smaller spaces.other smaller spaces.

Assuming that slope Assuming that slope AA is correct for the main is correct for the main room, persons room, persons subjected to slope subjected to slope BB would hear inferior would hear inferior sound.sound.

Electroacoustical CouplingElectroacoustical Coupling

What is the overall effect when sound What is the overall effect when sound picked up from a studio having one picked up from a studio having one reverberation time is reproduced in a reverberation time is reproduced in a listening room having a different listening room having a different reverberation time?reverberation time?

The combined reverb time is greater than The combined reverb time is greater than either aloneeither alone

If the reverb time of each room alone is If the reverb time of each room alone is the same, the combined reverb time is the same, the combined reverb time is 20.8% longer than one of them.20.8% longer than one of them.

Optimum Reverberation TimeOptimum Reverberation Time

The best reverb The best reverb time for a time for a space in which space in which music is played music is played depends on the depends on the size of the size of the space and the space and the type of music.type of music.

Spaces for Spaces for speech require speech require shorter reverb shorter reverb times than for times than for music.music.

Optimum Reverb Time Optimum Reverb Time ExamplesExamples

Optimum Reverb Time Optimum Reverb Time ExamplesExamples

Bass RiseBass Rise Taking the 1 kHz value as a reference, rises of 80% at Taking the 1 kHz value as a reference, rises of 80% at

63 Hz and 20% at 125 Hz were found to be acceptable 63 Hz and 20% at 125 Hz were found to be acceptable in studios designed for voice recording.in studios designed for voice recording.

Living Room Reverb TimesLiving Room Reverb Times

The The average average reverb reverb time time decreases decreases from 0.69 from 0.69 seconds at seconds at 125 Hz to 125 Hz to 0.4 0.4 seconds at seconds at 8 kHz.8 kHz.

The Sabine EquationThe Sabine Equation

The absorption coefficients published by materials The absorption coefficients published by materials manufacturers are typically Sabine coefficients and can manufacturers are typically Sabine coefficients and can

be applied directly in the Sabine equation.be applied directly in the Sabine equation.

Absorption and Absorption Absorption and Absorption CoefficientsCoefficients

Absorption:Absorption: in acoustics, the conversion of in acoustics, the conversion of sound energy to heat.sound energy to heat.

Absorption Coefficient:Absorption Coefficient: the fraction of the fraction of sound energy that is absorbed at any sound energy that is absorbed at any surface. It has a value between 0 and 1 surface. It has a value between 0 and 1 and varies with the frequency and angle of and varies with the frequency and angle of incidence of the sound.incidence of the sound.

Multiplying the surface area (in sq. ft.) by Multiplying the surface area (in sq. ft.) by the absorption coefficient results in the absorption coefficient results in absorption units (sabins).absorption units (sabins).

Reverberation CalculationsReverberation Calculations

The The diagram diagram shows an shows an example example of the of the RT60 RT60 calculatiocalculations using ns using the the Sabine Sabine equation.equation.

Reverb Time (RT60) Reverb Time (RT60) CalculationsCalculations

1) Calculate the total areas of each type of 1) Calculate the total areas of each type of surfacesurface

2) Find the absorption coefficients for each 2) Find the absorption coefficients for each type of surface for the six frequencies: 125 type of surface for the six frequencies: 125 Hz, 250 Hz, 500 Hz, 1 kHz, 2 kHz, & 4 kHzHz, 250 Hz, 500 Hz, 1 kHz, 2 kHz, & 4 kHz

3) Multiply the area by the coefficient to 3) Multiply the area by the coefficient to determine the absorption units (sabins)determine the absorption units (sabins)

4) Add all sabins to find total sabins for 4) Add all sabins to find total sabins for each frequencyeach frequency

5) Plug all info into the Sabine equation to 5) Plug all info into the Sabine equation to find the reverb time (RT60) for the room.find the reverb time (RT60) for the room.

Determining Room TreatmentsDetermining Room Treatments

The result of the The result of the RT60 calculations RT60 calculations show a short show a short reverb time at low reverb time at low frequencies, long frequencies, long reverb time in the reverb time in the midrange, and midrange, and medium reverb medium reverb time in the high time in the high frequencies.frequencies.

Determining Room TreatmentsDetermining Room Treatments

1) Find treatments that will achieve the 1) Find treatments that will achieve the desired responsedesired response

2) Determine how much treatment (in sq. 2) Determine how much treatment (in sq. ft.) would be necessary to add the desired ft.) would be necessary to add the desired amount of absorption (sabins) by dividing amount of absorption (sabins) by dividing the sabins by the absorption coefficient. the sabins by the absorption coefficient. The result will be the amount of treatment The result will be the amount of treatment in sq. ft.in sq. ft.